(../../../../../../../homepage.html) A Copper Alliance (http://copperalliance.org) MemberOptimization of Motor Rotor: Slot Shape, Frame Size,Rotor DiameterSLOT SHAPE

Designing Squirrel Cage Rotor Slots with High Conductivity

I. INTRODUCTION:

There has been, in recent years, an effort to make cast copper rotors for industrial useinduction motors. The objective is to make motors more efficient because of the higherconductivity of copper. In addition, the reduced losses in such motors may lead to betterdesign flexibility and therefore motors that are more compact.

In this paper we examine the tradeoff between running efficiency and starting performance.In order to understand how induction motors work it is necessary to have a good model forthe conduction properties of the conductors in the slots of the rotor. We employ a simplemodel that has been developed for this purpose. We propose to examine the frequencyresponse of the rotor bar impedance for indications of how the motor will work, taking intoaccount not only running efficiency and starting performance but also stray load losses whichare also affected by rotor bar impedance.

II. ROTOR IMPEDANCE

For illustration, Fig. 1 shows a comparison of torque vs. speed for two identical notionalinduction motors, differing only in the value of rotor resistance, commonly noted as R2. Thecharacteristic curve with higher resistance would, for all load torques, operate at a somewhatlower running speed (and hence higher slip and lower efficiency) than the machine with thelower resistance. On the other hand, starting torque is lower for the low resistance rotor andthis might lead to unsatisfactory performance in some applications.

The use of copper as the conductor of induction motor rotors would typically lead toimprovements in efficiency, relative to motors using aluminum. This is often done in largemotors in which squirrel cages are fabricated from bars of material brazed to end rings. Insuch machines it is common to employ 'starting' bars of higher resistivity material. Ourobjective here, however, is to discuss ways of designing rotor slots for fabrication by casting asingle material, as is commonly done with aluminum as the rotor conductor material.

Figure 1: Notional Torque Speed Curves

In some induction motors, what is called the 'deep bar' effect, or distribution of rotor currentsdue to eddy currents, is taken advantage of. When the rotor is stationary or turning slowly thefrequency of rotor currents is relatively high, the currents crowd to the top of the rotor barand the resistive part of impedance is relatively high.

Figure 2: Comparison of Slot Shapes

Shown in Fig. 2 are three different possible slot shapes. On the left is the shape used in theoriginal cast aluminum rotor. It has a characteristic tapered shape so that the teeth betweenrotor bars are of uniform section. It tapers toward the rotor surface.

Fig. 3 shows the real and reactive parts of the impedance of the slot designed for aluminumwith two different materials: aluminum and copper.

Figure 3: Aluminum and Copper Slot Resistance

The frequency range shown in Fig. 3 encompasses not only starting and running frequencies,but also the frequencies of currents in the rotor bars due to the various space harmonics ofthe stator winding. As can be seen in the figure, the copper rotor has substantially lowerresistance over the whole frequency range, but the difference is largest at running conditions.At higher frequencies the smaller skin depth of copper causes the impedance of those bars toincrease.

Now the question at hand is this: Can we shape the rotor bars to take advantage of the higherconductivity of copper to produce good running efficiency and yet have satisfactory startingperformance? We do not believe we have found the optimum bar shape yet, but we can atleast illustrate the question with a comparison of the other two bar shapes shown in Fig. 2.Fig. 4 shows a comparison of the slot resistance of those two bars over the same frequencyrange.

The first copper bar was designed with a narrow top within which the relatively high frequencycurrents of starting flow, producing a higher resistance at start. Note that this is only partiallysuccessful, as the second bar design, B actually results in larger resistance at starting. This isbecause the narrow slot between the top, starting bar and the rest of the conductor iseffective at isolating starting frequency currents to the starting bar. At the same time, notethat Bar A results in higher resistance at harmonic frequencies, indicating possibly higher strayload losses.

Figure 4: Comparison of two copper rotors (Slot A and Slot B ofFig. 2)

III. METHODOLOGY

Induction motors are represented for the purpose of design analysis by an equivalent circuitas shown in Fig. 5. Some components of the rotor leakages and resistances of each section arefrequency dependent and therefore functions of rotor frequency and so speed.

Figure 5. 'Alger' Equivalent Circuit Model

To establish rotor resistances and reactances we use a simple technique for representing therotor bar as a ladder network. The bar is divided into a relatively large number of slices,oriented in a direction perpendicular to the rotor surface. Each such slice is represented by asimple 'tee' circuit consisting of inductance, representing cross-slot flux and resistance,representing the current carried by that part of the slot.

Figure 6: Element Model

To find the values of the slot parameters make reference to Figure 7.

Figure 7. Illustration of calculation of slot parameters

Note that, from the Ampere's Law contour shown, magnetic field crossing the slot at somevertical position y is related to all current in the slot below that position. From the Faraday'sLaw contour we see that all of the inductance elements in the slot are in series and the electricfield (voltage per unit length) driving current is the sum of voltages across all inductiveelements below the position y. Then if we represent the slot as a series connection of basic'tee' elements, the inductance per unit length of a section is:

where d is the height of the section and w is width of the slot at thatposition. Resistance per unit length is:

where is material conductivity.

The tee elements are accordingly connected together as is shown in Fig. 8.

Figure 8: Ladder representation of slot impedance

A more sophisticated technique might have been used. A good example of this is the elegantformulation of Williamson using a finite element model for each slot embedded in a circuitmodel of the machine as shown in Fi.g 5 . In this case it was felt that the accuracy achieved bythe ladder network would probably be sufficient, and the resulting efficiency of calculationmakes it possible to draw some conclusions regarding optimization of the machine.

IV. SLOT REPRESENTATION

Many different types of slot shapes are possible in induction motors. In large machines it istypical to use slot shapes that both concentrate currents near the rotor surface and canwithstand the heating associated. It is also necessary to have enough conductor area near thesurface to produce relatively low loss at the belt and zigzag harmonic frequencies. For smallmotors we have had some success with the slot shape shown in Figure 9.

Figure 9: Modified Kite Form Bar Shape

Figure 10: Slot Geometry

Larger machines may require different bar forms. Figure 10 shows a geometry that has adiscrete 'starting bar' to carry high frequency currents at starting conditions plus a 'leakageslot' to magnetically isolate the starting bar from the main conductor under starting

conditions. This type of bar is shown in Figure 10.The 'main' part of the slot is a trapezoid thatis narrower at the bottom than at the top to allow for constant width of teeth between slots.The top and bottom part of the slot is bounded by semicircles of appropriate radius. The'leakage slot has radial height h and the starting bar has radius Rb. If we define the slot factorto be the ratio of slot width to slot pitch (slot plus tooth) at the top of the trapezoidal (main)part of the slot to be:

V. EXAMPLE MACHINE

To illustrate the impact of using copper in a machine we adopt a 5.5 kW, 50 Hz machine builtfor pump application so that starting torque is an important feature. The rotor slot we assumehere is similar to the slot in the actual machine (in which the starting bar is not exactlycylindrical as we assume. The bar is defined by a starting bar diameter of 4.2 mm, a leakageslot that is 3 mm high and 1 mm wide, 28 rotor bars in a rotor that is 110 mm in diameter anda ratio of inner to maximum slot widths of . The slot as constructed is shown in Fig. 11. Thehorizontal lines represent section widths.

Figure 11: Example Slot Shape

Using standard analysis techniques and the slot impedance estimation technique describedhere, we can estimate machine performance for cast aluminum and cast copper. The analysistechnique has been compared with the actual 5.5 kW motor and the results are reasonablyaccurate for both copper and aluminum rotor cages. The frequency response for the twoconductors is shown in Fig. 12 and the Torque-speed curves are shown in Fig. 13.

Figure 12. Frequency Response Comparison: Aluminum Vs.Copper

Figure 13: Comparison of copper vs. aluminum in 5.5 kW motor

In this machine the copper rotor achieves better performance by taking advantage of the deepbar effect to maintain starting torque while still improving efficiency (89.8% vs 87% for Al).

VI: TRADE STUDY

In an attempt to understand how variations in slot geometry might affect machineperformance a short parametric trade was carried out by varying the starting bar diameterfrom 2 to 10 mm, holding the leakage slot geometry constant, and then varying the leakageslot height from 1 to 5 mm while holding the starting bar diameter at 4.2 mm. The resultingextremes of slot geometry are shown in Fig. 14 and 15.

Figure 14: Slot Geometry Varying Starting Bar

Machine performance has been estimated for the ranges of slot geometries shown in Fig. 14and 15, assuming copper to be the cage material. Selected performance parameters areshown in Fig. 16 and 17. Fig. 16 shows variation of efficiency and starting torque over variationof starting bar radius, holding the other defining parameters constant.

Figure 15: Slot Geometry Varying Leakage Slot Height

Figure 16: Parametric Study vs. Starting Bar Diameter

Figure 17: Parametric Study vs. Leakage Slot Height

In the case of leakage bar height there is a tradeoff: increasing the leakage height consistentlyincreases starting torque while also consistently reducing efficiency. This is to be expected asincreasing the rotor leakage height pushes the main part of the slot down and reducesavailable slot width, leaving less conductor in running conditions and increasing runningresistance. On the other hand, increasing the starting bar diameter seems to consistentlyincrease efficiency as it increases total conductor available. There is, however, a maximumstarting torque at a bar diameter very close to the diameter of the example machine.

VII. CONCLUSIONS

This brief study is an attempt to understand how to make appropriate use of differentconducting materials in the squirrel cages of cast rotors. In particular, we were interested inhow to properly use the higher conductivity of copper in such motors.

As should be clear, the higher conductivity of copper increases skin effect and thereforemakes deep bar and multiple cage effects more pronounced. This can be seen from thefrequency response plots that examine the impedance per unit length of the rotor slots. Highfrequency impedance of the rotor slots has an impact on stray load and no-load losses.Medium frequency (around line frequency) impedance effects starting performance. Lowfrequency impedance (about slip frequency) affects running efficiency. While this has been

known for some time, the frequency response plots shown here allow for visualization ofthese effects. They can tell why a narrow conductor filled slot above the main bar is probablynot as effective as a starting bar with a narrower leakage bar below.

We have also confirmed the adequacy of calculating rotor cage impedances using a simpleflux tube (one dimensional finite element) model for simple trade studies.

______________________________

i. Modeling of Rotor bars with Skin Effect for Dynamic Simulation of Induction Machines, J.Langheim, Conference Record, IEEE Industry Applications Society Annual Meeting, 1989,pp 38-44.

ii. Induction Machines, Philip Alger, Gordon and Breach, 1970. This is actually an extentionto Alger's model, explained in Electric Motor Handbook, H. Wayne Beaty et al. McGrawHill, 1998

iii. Calculation of cage induction motor equivalent circuit parameters using finite elements,S. Williamson, M.J. Robinson, Proc. IEE (Part B) Vol 138, No. 5 pp 264-276, (1991)

FRAME SIZE AND ROTOR DIAMETER

SEW-Eurodrive, a large manufacturer of industrial drive systems, has made the CRM anintegral part of a broad range of drive motors upgraded to European efficiency classificationEFF1 (50 Hz) and EPAct (60 Hz) efficiencies. Their studies indicated that in many instances, theefficiency increase permitted use of the same frame size with a copper rotor as the currentproduction aluminum rotor (Brush 2002, Kimmich 2005). Design studies showed that the EFF1aluminum rotor motor would require moving up one frame size and would require increasingthe size of the entire motor/gear package. This would be expensive and had the additionaldisadvantage of making retrofitting with a more efficient motor impossible. In the redesign ofthe motor lines to EFF1, direct substitution of copper for aluminum was found to meet theobjectives for the smaller motors while the larger motors were entirely redesigned to bestutilize the copper. The copper redesigns maintained the outside motor dimensions andachieved the desired torque at various points on the torque-load curve and controlled the in-rush currents in the starting region.

Table 1 presents efficiency data for four SEW aluminum and copper rotor motors at 60 Hz. The1.5 Hp motors essentially have the same layout of stator and rotor laminations; i.e. thealuminum rotor bars have simply been replaced by the die-cast copper. But the laminationsteel has been upgraded from material with losses of 8 W/kg to a better grade with lossesrated at 4 W/kg. In contrast, the high efficiency larger motors have a completely newlamination and stator design. The design modifications relate to the starting behaviordiscussed below. The data in Table 1 show that the copper rotor leads to a significant increasein efficiency.

In taking the decision to use copper in the rotor for this series of industrial drive motors toreach EFF1 minimum efficiencies, SEW conducted an extensive modeling study comparing thesize, weight and overall costs of motors of equivalent efficiency using aluminum in the rotor.The finding was that, for the motors discussed here, the use of copper in the rotor cageallowed reductions in rotor diameter, in iron required for laminations and in stator copperwindings. The copper rotor motors are one frame size smaller than the the aluminum rotordesign would have allowed. Overall there was an accompanying reduction in totalmanufacturing costs; the cost of the motor with an aluminum rotor at a given EFF1 efficiency

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ranged from similar to 15% higher than the copper version. In these examples, weight savingsof up to 18% and cost savings of up to 15% were effected. This cost saving for the copper rotormotor was in spite of the die-casting component of the copper rotor being typically threetimes more costly than the aluminum rotor.

Analysis by U.S. manufacturers of 7.5 and 15 Hp motors and assembled by CDA as acomposite equivalent U.S. motor meeting EPAct efficiency standards came to similarconclusions. The die-cast copper rotor motors would be 18 to 20% lighter and 14 to 18% lessexpensive to build than the aluminum rotor motor at the same efficiency when a frame sizereduction was possible. When a frame size reduction was not possible, reductions and weightand cost were still indicated in the design studies, but the percentage reductions were in thesingle digits for the copper rotor machine.